Neural Circuits for Fast Poisson Compressed Sensing in the Olfactory Bulb.

Within a single sniff, the mammalian olfactory system can decode the identity and concentration of odorants wafted on turbulent plumes of air. Yet, it must do so given access only to the noisy, dimensionally-reduced representation of the odor world provided by olfactory receptor neurons. As a result, the olfactory system must solve a compressed sensing problem, relying on the fact that only a handful of the millions of possible odorants are present in a given scene. Inspired by this principle, past works have proposed normative compressed sensing models for olfactory decoding. However, these models have not captured the unique anatomy and physiology of the olfactory bulb, nor have they shown that sensing can be achieved within the 100-millisecond timescale of a single sniff. Here, we propose a rate-based Poisson compressed sensing circuit model for the olfactory bulb. This model maps onto the neuron classes of the olfactory bulb, and recapitulates salient features of their connectivity and physiology. For circuit sizes comparable to the human olfactory bulb, we show that this model can accurately detect tens of odors within the timescale of a single sniff. We also show that this model can perform Bayesian posterior sampling for accurate uncertainty estimation. Fast inference is possible only if the geometry of the neural code is chosen to match receptor properties, yielding a distributed neural code that is not axis-aligned to individual odor identities. Our results illustrate how normative modeling can help us map function onto specific neural circuits to generate new hypotheses.

Contrasting random and learned features in deep Bayesian linear regression.

Understanding how feature learning affects generalization is among the foremost goals of modern deep learning theory. Here, we study how the ability to learn representations affects the generalization performance of a simple class of models: deep Bayesian linear neural networks trained on unstructured Gaussian data. By comparing deep random feature models to deep networks in which all layers are trained, we provide a detailed characterization of the interplay between width, depth, data density, and prior mismatch. We show that both models display samplewise double-descent behavior in the presence of label noise. Random feature models can also display modelwise double descent if there are narrow bottleneck layers, while deep networks do not show these divergences. Random feature models can have particular widths that are optimal for generalization at a given data density, while making neural networks as wide or as narrow as possible is always optimal. Moreover, we show that the leading-order correction to the kernel-limit learning curve cannot distinguish between random feature models and deep networks in which all layers are trained. Taken together, our findings begin to elucidate how architectural details affect generalization performance in this simple class of deep regression models.

Excitatory and inhibitory neural dynamics jointly tune motion detection.

Neurons integrate excitatory and inhibitory signals to produce their outputs, but the role of input timing in this integration remains poorly understood. Motion detection is a paradigmatic example of this integration, since theories of motion detection rely on different delays in visual signals. These delays allow circuits to compare scenes at different times to calculate the direction and speed of motion. Different motion detection circuits have different velocity sensitivity, but it remains untested how the response dynamics of individual cell types drive this tuning. Here, we sped up or slowed down specific neuron types in Drosophila's motion detection circuit by manipulating ion channel expression. Altering the dynamics of individual neuron types upstream of motion detectors increased their sensitivity to fast or slow visual motion, exposing distinct roles for excitatory and inhibitory dynamics in tuning directional signals, including a role for the amacrine cell CT1. A circuit model constrained by functional data and anatomy qualitatively reproduced the observed tuning changes. Overall, these results reveal how excitatory and inhibitory dynamics together tune a canonical circuit computation.

On Neural Network Kernels and the Storage Capacity Problem.

In this short note, we reify the connection between work on the storage capacity problem in wide two-layer treelike neural networks and the rapidly growing body of literature on kernel limits of wide neural networks. Concretely, we observe that the "effective order parameter" studied in the statistical mechanics literature is exactly equivalent to the infinite-width neural network gaussian process kernel. This correspondence connects the expressivity and trainability of wide two-layer neural networks.

Parallel locomotor control strategies in mice and flies.

Our understanding of the neural basis of locomotor behavior can be informed by careful quantification of animal movement. Classical descriptions of legged locomotion have defined discrete locomotor gaits, characterized by distinct patterns of limb movement. Recent technical advances have enabled increasingly detailed characterization of limb kinematics across many species, imposing tighter constraints on neural control. Here, we highlight striking similarities between coordination patterns observed in two genetic model organisms: the laboratory mouse and Drosophila. Both species exhibit continuously-variable coordination patterns with similar low-dimensional structure, suggesting shared principles for limb coordination and descending neural control.

Drifting neuronal representations: Bug or feature?

The brain displays a remarkable ability to sustain stable memories, allowing animals to execute precise behaviors or recall stimulus associations years after they were first learned. Yet, recent long-term recording experiments have revealed that single-neuron representations continuously change over time, contravening the classical assumption that learned features remain static. How do unstable neural codes support robust perception, memories, and actions? Here, we review recent experimental evidence for such representational drift across brain areas, as well as dissections of its functional characteristics and underlying mechanisms. We emphasize theoretical proposals for how drift need not only be a form of noise for which the brain must compensate. Rather, it can emerge from computationally beneficial mechanisms in hierarchical networks performing robust probabilistic computations.

Natural gradient enables fast sampling in spiking neural networks.

For animals to navigate an uncertain world, their brains need to estimate uncertainty at the timescales of sensations and actions. Sampling-based algorithms afford a theoretically-grounded framework for probabilistic inference in neural circuits, but it remains unknown how one can implement fast sampling algorithms in biologically-plausible spiking networks. Here, we propose to leverage the population geometry, controlled by the neural code and the neural dynamics, to implement fast samplers in spiking neural networks. We first show that two classes of spiking samplers-efficient balanced spiking networks that simulate Langevin sampling, and networks with probabilistic spike rules that implement Metropolis-Hastings sampling-can be unified within a common framework. We then show that careful choice of population geometry, corresponding to the natural space of parameters, enables rapid inference of parameters drawn from strongly-correlated high-dimensional distributions in both networks. Our results suggest design principles for algorithms for sampling-based probabilistic inference in spiking neural networks, yielding potential inspiration for neuromorphic computing and testable predictions for neurobiology.

Activation function dependence of the storage capacity of treelike neural networks.

The expressive power of artificial neural networks crucially depends on the nonlinearity of their activation functions. Though a wide variety of nonlinear activation functions have been proposed for use in artificial neural networks, a detailed understanding of their role in determining the expressive power of a network has not emerged. Here, we study how activation functions affect the storage capacity of treelike two-layer networks. We relate the boundedness or divergence of the capacity in the infinite-width limit to the smoothness of the activation function, elucidating the relationship between previously studied special cases. Our results show that nonlinearity can both increase capacity and decrease the robustness of classification, and provide simple estimates for the capacity of networks with several commonly used activation functions. Furthermore, they generate a hypothesis for the functional benefit of dendritic spikes in branched neurons.

Statistical structure of the trial-to-trial timing variability in synfire chains.

Timing and its variability are crucial for behavior. Consequently, neural circuits that take part in the control of timing and in the measurement of temporal intervals have been the subject of much research. Here we provide an analytical and computational account of the temporal variability in what is perhaps the most basic model of a timing circuit-the synfire chain. First we study the statistical structure of trial-to-trial timing variability in a reduced but analytically tractable model: a chain of single integrate-and-fire neurons. We show that this circuit's variability is well described by a generative model consisting of local, global, and jitter components. We relate each of these components to distinct neural mechanisms in the model. Next we establish in simulations that these results carry over to a noisy homogeneous synfire chain. Finally, motivated by the fact that a synfire chain is thought to underlie the circuit that takes part in the control and timing of the zebra finch song, we present simulations of a biologically realistic synfire chain model of the zebra finch timekeeping circuit. We find the structure of trial-to-trial timing variability to be consistent with our previous findings and to agree with experimental observations of the song's temporal variability. Our study therefore provides a possible neuronal account of behavioral variability in zebra finches.

Spatiotemporally precise optogenetic activation of sensory neurons in freely walking Drosophila.

Previous work has characterized how walking Drosophila coordinate the movements of individual limbs (DeAngelis et al., 2019). To understand the circuit basis of this coordination, one must characterize how sensory feedback from each limb affects walking behavior. However, it has remained difficult to manipulate neural activity in individual limbs of freely moving animals. Here, we demonstrate a simple method for optogenetic stimulation with body side-, body segment-, and limb-specificity that does not require real-time tracking. Instead, we activate at random, precise locations in time and space and use post hoc analysis to determine behavioral responses to specific activations. Using this method, we have characterized limb coordination and walking behavior in response to transient activation of mechanosensitive bristle neurons and sweet-sensing chemoreceptor neurons. Our findings reveal that activating these neurons has opposite effects on turning, and that activations in different limbs and body regions produce distinct behaviors.

A minimal synaptic model for direction selective neurons in Drosophila.

Visual motion estimation is a canonical neural computation. In Drosophila, recent advances have identified anatomic and functional circuitry underlying direction-selective computations. Models with varying levels of abstraction have been proposed to explain specific experimental results but have rarely been compared across experiments. Here we use the wealth of available anatomical and physiological data to construct a minimal, biophysically inspired synaptic model for Drosophila's first-order direction-selective T4 cells. We show how this model relates mathematically to classical models of motion detection, including the Hassenstein-Reichardt correlator model. We used numerical simulation to test how well this synaptic model could reproduce measurements of T4 cells across many datasets and stimulus modalities. These comparisons include responses to sinusoid gratings, to apparent motion stimuli, to stochastic stimuli, and to natural scenes. Without fine-tuning this model, it sufficed to reproduce many, but not all, response properties of T4 cells. Since this model is flexible and based on straightforward biophysical properties, it provides an extensible framework for developing a mechanistic understanding of T4 neural response properties. Moreover, it can be used to assess the sufficiency of simple biophysical mechanisms to describe features of the direction-selective computation and identify where our understanding must be improved.

Using slow frame rate imaging to extract fast receptive fields.

In functional imaging, large numbers of neurons are measured during sensory stimulation or behavior. This data can be used to map receptive fields that describe neural associations with stimuli or with behavior. The temporal resolution of these receptive fields has traditionally been limited by image acquisition rates. However, even when acquisitions scan slowly across a population of neurons, individual neurons may be measured at precisely known times. Here, we apply a method that leverages the timing of neural measurements to find receptive fields with temporal resolutions higher than the image acquisition rate. We use this temporal super-resolution method to resolve fast voltage and glutamate responses in visual neurons in Drosophila and to extract calcium receptive fields from cortical neurons in mammals. We provide code to easily apply this method to existing datasets. This method requires no specialized hardware and can be used with any optical indicator of neural activity.

Dynamic nonlinearities enable direction opponency in Drosophila elementary motion detectors.

Direction-selective neurons respond to visual motion in a preferred direction. They are direction-opponent if they are also inhibited by motion in the opposite direction. In flies and vertebrates, direction opponency has been observed in second-order direction-selective neurons, which achieve this opponency by subtracting signals from first-order direction-selective cells with opposite directional tunings. Here, we report direction opponency in Drosophila that emerges in first-order direction-selective neurons, the elementary motion detectors T4 and T5. This opponency persists when synaptic output from these cells is blocked, suggesting that it arises from feedforward, not feedback, computations. These observations exclude a broad class of linear-nonlinear models that have been proposed to describe direction-selective computations. However, they are consistent with models that include dynamic nonlinearities. Simulations of opponent models suggest that direction opponency in first-order motion detectors improves motion discriminability by suppressing noise generated by the local structure of natural scenes.

The manifold structure of limb coordination in walking Drosophila.

Terrestrial locomotion requires animals to coordinate their limb movements to efficiently traverse their environment. While previous studies in hexapods have reported that limb coordination patterns can vary substantially, the structure of this variability is not yet well understood. Here, we characterized the symmetric and asymmetric components of variation in walking kinematics in the genetic model organism Drosophila. We found that Drosophila use a single continuum of coordination patterns without evidence for preferred configurations. Spontaneous symmetric variability was associated with modulation of a single control parameter-stance duration-while asymmetric variability consisted of small, limb-specific modulations along multiple dimensions of the underlying symmetric pattern. Commands that modulated walking speed, originating from artificial neural activation or from the visual system, evoked modulations consistent with spontaneous behavior. Our findings suggest that Drosophila employ a low-dimensional control architecture, which provides a framework for understanding the neural circuits that regulate hexapod legged locomotion.